Sequential estimation in the group testing problem

Using group testing in a two-phase epidemiologic design to identify the effects of a large number of antibody reactions on disease risk

BACKGROUND

The role of immunological responses to exposed bacteria on disease incidence is increasingly under investigation. With many bacterial species, and many potential antibody reactions to a particular species, the large number of assays required for this type of discovery can make it prohibitively expensive. We propose a two-phase group testing design to more efficiently screen numerous antibody effects in a case-control setting.

METHODS

Phase 1 uses group testing to select antibodies that are differentially expressed between cases and controls. The selected antibodies go on to Phase 2 individual testing.

RESULTS

We evaluate the two-phase group testing design through simulations and example data and find that it substantially reduces the number of assays required relative to standard case-control and group testing designs, while maintaining similar statistical properties.

CONCLUSION

The proposed two-phase group testing design can dramatically reduce the number of assays required, while providing comparable results to a case-control design.

Determination of Varying Group Sizes for Pooling Procedure

Pooling is an attractive strategy in screening infected specimens, especially for rare diseases. An essential step of performing the pooled test is to determine the group size. Sometimes, equal group size is not appropriate due to population heterogeneity. In this case, varying group sizes are preferred and could be determined while individual information is available. In this study, we propose a sequential procedure to determine varying group sizes through fully utilizing available information. This procedure is data driven. Simulations show that it has good performance in estimating parameters.

Efficient methods for the estimation of the multinomial parameter for the two-trait group testing model

Estimation of a single Bernoulli parameter using pooled sampling is among the oldest problems in the group testing literature. To carry out such estimation, an array of efficient estimators have been introduced covering a wide range of situations routinely encountered in applications. More recently, there has been growing interest in using group testing to simultaneously estimate the joint probabilities of two correlated traits using a multinomial model. Unfortunately, basic estimation results, such as the maximum likelihood estimator (MLE), have not been adequately addressed in the literature for such cases. In this paper, we show that finding the MLE for this problem is equivalent to maximizing a multinomial likelihood with a restricted parameter space. A solution using the EM algorithm is presented which is guaranteed to converge to the global maximizer, even on the boundary of the parameter space. Two additional closed form estimators are presented with the goal of minimizing the bias and/or mean square error. The methods are illustrated by considering an application to the joint estimation of transmission prevalence for two strains of the Potato virus Y by the aphid Myzus persicae.

Revisiting Nested Group Testing Procedures: New Results, Comparisons, and Robustness

Group testing has its origin in the identification of syphilis in the U.S. army during World War II. Much of the theoretical framework of group testing was developed starting in the late 1950s, with continued work into the 1990s. Recently, with the advent of new laboratory and genetic technologies, there has been an increasing interest in group testing designs for cost saving purposes. In this article, we compare different nested designs, including Dorfman, Sterrett and an optimal nested procedure obtained through dynamic programming. To elucidate these comparisons, we develop closed-form expressions for the optimal Sterrett procedure and provide a concise review of the prior literature for other commonly used procedures. We consider designs where the prevalence of disease is known as well as investigate the robustness of these procedures, when it is incorrectly assumed. This article provides a technical presentation that will be of interest to researchers as well as from a pedagogical perspective. Supplementary material for this article available online.